Skunks can are extraordinarily destructive and annoying at the same time. They ruin gardens by eating flowers and lawn by burrowing in and out. This can be destructive to your house foundation when they get to it. Their defense mechanism of spraying anything that they view as a threat and in this case you will demand a lot of care while getting rid of them. The best way is to make your compound non-habitable for the skunks and denying them what they want out of it.
Make food in accessible to skunks as this might be one of the things that are attracting them to your property. Cover all trash cans with tight lids to ensure that they cannot get into them. Compost pits too should be covered to also deny them a place to harbour.
Soak rags in ammonia and place them on either ends of they burrow holes that the skunks use. The smell is a repellent to them and will do their best to avoid it hence vacate your premises.
You could use traps is necessary. The wire traps are ideal in this method as they just trap the skunk but not kill it. Place the trap on one end of the burrow holes and wait for it to get caught. After you have caught it, relocate it to some far away place from your home and release it. To know which hole they use most, place some leaves and check later if they have been moved.
Fumigants, in this case gas cartridges have been known to get rid of the skunk. The smell is repulsive to them and might decide to leave your property and find another place to harbour.
You should know that shooting skunks is not advisable as some species are protected; dotted skunks are an excellent example. Killing them might land you in to problems with the authority.
Learn more about skunk removal.